Moving to a new server...

Our current host is going out of business. Luckily we already have a new host lined up but as I stated before, I've just been brought into this WMH/cPanel world from another area and it isn't my main expertise.

What is the best way to migrate everything from one server to another?

I would recommend:
1) Copy the EasyApache profile from the old server and run it on the new server.
2) Go into the account transfer utility and copy every single account. The account transfer transfers absolutely all cPanel settings.

This way no root access muddling is required

Note that this transfer might break Rails apps and Tomcat servlet configurations. From my experience, it is quite reliable.